One of the first polls since President Donald Trump's former attorney implicated him in illegal activity was released Tuesday, and most of the results were not very good for the president.

A poll from Quinnipiac University found 64 percent of American voters believe Trump committed crimes before assuming office, while 24 percent did not believe he had (another 13 percent said they weren't sure.) Forty-five percent said they think Trump committed crimes since taking office, compared with 43 percent who believe he did not.

The numbers among Republicans were better for the president: One-third said they believe he committed crimes before taking office, and 48 percent said he did not. Only 12 percent of Republicans said Trump had committed crimes since taking office; 79 percent said he did not.

In the poll, just 44 percent of respondents believed Cohen told the truth in his testimony before the House Oversight and Reform Committee. But half of them said they believed Cohen over Trump. Fifty-eight percent said Congress should do more to investigate Cohen's allegations.

"When two-thirds of voters think you have committed a crime in your past life, and almost half of voters say it's a toss-up over whether you committed a crime while in the Oval Office, confidence in your overall integrity is very shaky," said Tim Malloy, assistant director of the Quinnipiac University Poll. "Add to that, Michael Cohen, a known liar headed to the big house, has more credibility than the leader of the free world."

Only 30 percent of voters said they believe the president is honest, although two-thirds of Republicans said he is trustworthy (95 percent of Democrats disagreed). Twenty-two percent of voters said they consider Trump a good role model for children, compared with 54 percent of Republicans who said they think he is a good role model.

The good news for the president: Despite high numbers of voters saying they suspect him of illegal activity, only 35 percent said Congress should begin impeachment proceedings; 59 percent said it should not.

Overall, the poll found Trump's job approval rating among voters was at 38 percent; 56 percent of voters said they disapproved of his performance. That number stood in contrast to other recent polls that had placed the president's approval rating in the mid- to low 40s.

It is too early to tell if the Quinnipiac poll – which tends to find Trump's approval rating lower than his polling average – is an outlier or a signal that Cohen's testimony is having an impact.

Trump's approval rating in the poll mirrored that of congressional Democrats. Thirty-eight percent of voters said they approved of the job Democrats are doing, and 56 percent said they disapproved. Congressional Republicans had a 27 percent approval rating, while 66 percent said they disapproved of the job they were doing.

The poll was conducted March 1-4 from among 1,120 voters and had a margin of error of plus or minus 3.4 percentage points.

Supporters cheer for U.S. President Donald Trump during CPAC 2019 on March 02, 2019 National Harbor, Md. The American Conservative Union hosts the annual Conservative Political Action Conference to discuss conservative agenda. Tasos Katopodis, Getty Images

President Donald J. Trump speaks at the 46th annual Conservative Political Action Conference (CPAC) at the Gaylord National Resort & Convention Center in National Harbor, Md., on March 2, 2019. Trump spoke on the final day of the four-day American Conservative Union's CPAC conference. Erik S. Lesser, EPA-EFE

President Donald J. Trump speaks at the 46th annual Conservative Political Action Conference (CPAC) at the Gaylord National Resort & Convention Center in National Harbor, Md., on March 2, 2019. Trump spoke on the final day of the four-day American Conservative Union's CPAC conference. Erik S. Lesser, EPA-EFE